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The science
Terminal settling velocity
A sphere reaches the speed at which weight minus buoyancy equals drag: (π/6) d³ (ρp − ρw) g = ½ CD ρw (π/4) d² v², with the Schiller-Naumann drag law CD = (24/Re)(1 + 0.15 Re0.687) and Re = ρw v d / μ. For small grains this reduces to Stokes' law v = g d² (ρp − ρw) / (18 μ). Water viscosity follows the Vogel relation μ = 2.414×10−5 10247.8/(T+133.15) Pa s.
Classification by up-flow
A grain moves with net speed U + w (w is its own settling velocity, negative when it sinks) plus random turbulent diffusion D. The chance of leaving by the top before the bottom, starting at height y0 in a column of length L, is exactly (1 − e−(U+w) y0/D) / (1 − e−(U+w) L/D). Amber (about 1080 kg/m³) is only slightly denser than fresh water and sinks, but it floats in any brine denser than the amber itself (real separation plants use saturated salt solutions of about 1200 kg/m³), while quartz sand (2650 kg/m³) sinks in either. Brine viscosity is approximated as μ × (1 + 0.0045 (ρw − 998)).
Honest simplifications: dilute suspension (no hindered settling), spherical grains, uniform up-flow, constant turbulent dispersion, brine viscosity from a linear fit, no electrostatic or surface effects. The 3D page shows the hydraulic washing process; this page isolates the physics that sorts the grains.
What to try
- Press Fresh water: amber now sinks like the sand and the separation fails.
- Press Up-flow too strong: sand is washed out with the amber and purity collapses.
- Press Dense brine, cold: higher viscosity slows every grain.